%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET684+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:41:39 PM UTC 2026
% Result : Theorem 3.86s 1.55s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 19
% Syntax : Number of formulae : 158 ( 17 unt; 9 def)
% Number of atoms : 770 ( 8 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1077 ( 465 ~; 431 |; 118 &)
% ( 20 <=>; 41 =>; 0 <=; 2 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-5 aty)
% Number of variables : 283 ( 0 sgn 235 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X0,X4),X2)
& member(ordered_pair(X4,X1),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f26,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> compose5(X0,X1,X2,X3,X4) = compose(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f29,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
fof(f30,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<=> ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_51) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<=> ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<~> ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) ) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f31]) ).
fof(f33,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<~> ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) ) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f32]) ).
fof(f39,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& member(X3,X1) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& member(X3,X1) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X0,X4),X2)
& member(ordered_pair(X4,X1),X3) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2)) )
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f26]) ).
fof(f62,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f68,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ ilf_type(X7,member_type(X1))
| ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f69,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ ilf_type(X7,member_type(X1))
| ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ ilf_type(X7,member_type(X1))
| ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X8] :
( ilf_type(X8,member_type(X1))
& member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
( ( ! [X7] :
( ~ ilf_type(X7,member_type(sK1))
| ~ member(ordered_pair(sK5,X7),sK3)
| ~ member(ordered_pair(X7,sK6),sK4) )
| ~ member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) )
& ( ( ilf_type(sK7,member_type(sK1))
& member(ordered_pair(sK5,sK7),sK3)
& member(ordered_pair(sK7,sK6),sK4) )
| member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) )
& ilf_type(sK6,member_type(sK2))
& ilf_type(sK5,member_type(sK0))
& ilf_type(sK4,relation_type(sK1,sK2))
& ilf_type(sK3,relation_type(sK0,sK1))
& ~ empty(sK2)
& ilf_type(sK2,set_type)
& ~ empty(sK1)
& ilf_type(sK1,set_type)
& ~ empty(sK0)
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X8,sK7)],[f70]) ).
fof(f82,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f39]) ).
fof(f83,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK13(X0),X0)
& ilf_type(sK13(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X1,sK13(X0))],[f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f41]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3) ) )
& ( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X0,X4),X2)
& member(ordered_pair(X4,X1),X3) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f44]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3) ) )
& ( ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X0,X5),X2)
& member(ordered_pair(X5,X1),X3) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3) ) )
& ( ( ilf_type(sK14(X0,X1,X2,X3),set_type)
& member(ordered_pair(X0,sK14(X0,X1,X2,X3)),X2)
& member(ordered_pair(sK14(X0,X1,X2,X3),X1),X3) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X5,sK14(X0,X1,X2,X3))],[f87]) ).
fof(f93,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f62]) ).
fof(f94,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f93]) ).
fof(f103,plain,
ilf_type(sK3,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f71]) ).
fof(f104,plain,
ilf_type(sK4,relation_type(sK1,sK2)),
inference(cnf_transformation,[],[f71]) ).
fof(f107,plain,
( member(ordered_pair(sK7,sK6),sK4)
| member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f108,plain,
( member(ordered_pair(sK5,sK7),sK3)
| member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f110,plain,
! [X7] :
( ~ ilf_type(X7,member_type(sK1))
| ~ member(ordered_pair(sK5,X7),sK3)
| ~ member(ordered_pair(X7,sK6),sK4)
| ~ member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f111,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f29]) ).
fof(f127,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f131,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f85]) ).
fof(f133,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f43]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(sK14(X0,X1,X2,X3),X1),X3)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,sK14(X0,X1,X2,X3)),X2)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ilf_type(sK14(X0,X1,X2,X3),set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
fof(f137,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
fof(f146,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X1,X2))
| compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f148,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f55]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f61]) ).
fof(f158,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f170,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(duplicate_literal_removal,[],[f158]) ).
fof(f186,definition,
( spl19_4
<=> member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f187,plain,
( ~ member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4))
| spl19_4 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f188,plain,
( member(ordered_pair(sK5,sK6),compose5(sK0,sK1,sK2,sK3,sK4))
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f190,definition,
( spl19_5
<=> member(ordered_pair(sK7,sK6),sK4) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f192,plain,
( member(ordered_pair(sK7,sK6),sK4)
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( spl19_4
| spl19_5 ),
inference(avatar_split_clause,[],[f107,f190,f186]) ).
fof(f195,definition,
( spl19_6
<=> member(ordered_pair(sK5,sK7),sK3) ),
introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition]) ).
fof(f197,plain,
( member(ordered_pair(sK5,sK7),sK3)
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( spl19_4
| spl19_6 ),
inference(avatar_split_clause,[],[f108,f195,f186]) ).
fof(f205,definition,
( spl19_8
<=> ! [X7] :
( ~ ilf_type(X7,member_type(sK1))
| ~ member(ordered_pair(X7,sK6),sK4)
| ~ member(ordered_pair(sK5,X7),sK3) ) ),
introduced(definition,[new_symbols(definition,[spl19_8])],[avatar_definition]) ).
fof(f206,plain,
( ! [X7] :
( ~ member(ordered_pair(sK5,X7),sK3)
| ~ member(ordered_pair(X7,sK6),sK4)
| ~ ilf_type(X7,member_type(sK1)) )
| ~ spl19_8 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f207,plain,
( ~ spl19_4
| spl19_8 ),
inference(avatar_split_clause,[],[f110,f205,f186]) ).
fof(f219,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(resolution,[],[f170,f111]) ).
fof(f412,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(resolution,[],[f148,f155]) ).
fof(f413,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0) ),
inference(duplicate_literal_removal,[],[f412]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f413,f111]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f414,f111]) ).
fof(f491,definition,
( spl19_17
<=> relation_like(sK3) ),
introduced(definition,[new_symbols(definition,[spl19_17])],[avatar_definition]) ).
fof(f492,plain,
( relation_like(sK3)
| ~ spl19_17 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f493,plain,
( ~ relation_like(sK3)
| spl19_17 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f500,definition,
( spl19_19
<=> relation_like(sK4) ),
introduced(definition,[new_symbols(definition,[spl19_19])],[avatar_definition]) ).
fof(f501,plain,
( relation_like(sK4)
| ~ spl19_19 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f502,plain,
( ~ relation_like(sK4)
| spl19_19 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f634,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(sK14(X0,X1,X2,X3),X4)
| ~ ilf_type(X3,relation_type(X4,X5))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,X1,X2,X3),set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(resolution,[],[f134,f133]) ).
fof(f644,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(sK14(X0,X1,X2,X3),X4)
| ~ ilf_type(X3,relation_type(X4,X5))
| ~ ilf_type(sK14(X0,X1,X2,X3),set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(duplicate_literal_removal,[],[f634]) ).
fof(f652,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(sK14(X0,X1,X2,X3),X4)
| ~ ilf_type(X3,relation_type(X4,X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ),
inference(forward_subsumption_resolution,[],[f644,f136]) ).
fof(f657,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(sK14(X0,X1,X2,X3),X4)
| ~ ilf_type(X3,relation_type(X4,X5))
| ~ ilf_type(X5,set_type) ),
inference(forward_subsumption_resolution,[],[f652,f111]) ).
fof(f662,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(sK14(X0,X1,X2,X3),X4)
| ~ ilf_type(X3,relation_type(X4,X5)) ),
inference(forward_subsumption_resolution,[],[f657,f111]) ).
fof(f667,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| member(sK14(X0,X1,X2,X3),X4)
| ~ ilf_type(X3,relation_type(X4,X5)) ),
inference(forward_subsumption_resolution,[],[f662,f111]) ).
fof(f671,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| member(sK14(X0,X1,X2,X3),X4)
| ~ ilf_type(X3,relation_type(X4,X5)) ),
inference(forward_subsumption_resolution,[],[f667,f111]) ).
fof(f714,plain,
! [X0,X1] :
( compose5(X0,sK1,sK2,X1,sK4) = compose(X1,sK4)
| ~ ilf_type(X1,relation_type(X0,sK1))
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f146,f104]) ).
fof(f719,plain,
! [X0,X1] :
( compose5(X0,sK1,sK2,X1,sK4) = compose(X1,sK4)
| ~ ilf_type(X1,relation_type(X0,sK1))
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK1,set_type) ),
inference(forward_subsumption_resolution,[],[f714,f111]) ).
fof(f723,plain,
! [X0,X1] :
( compose5(X0,sK1,sK2,X1,sK4) = compose(X1,sK4)
| ~ ilf_type(X1,relation_type(X0,sK1))
| ~ ilf_type(sK2,set_type) ),
inference(forward_subsumption_resolution,[],[f719,f111]) ).
fof(f727,plain,
! [X0,X1] :
( ~ ilf_type(X1,relation_type(X0,sK1))
| compose5(X0,sK1,sK2,X1,sK4) = compose(X1,sK4) ),
inference(forward_subsumption_resolution,[],[f723,f111]) ).
fof(f732,plain,
compose5(sK0,sK1,sK2,sK3,sK4) = compose(sK3,sK4),
inference(resolution,[],[f727,f103]) ).
fof(f742,plain,
( ! [X0,X1] :
( ~ ilf_type(sK7,set_type)
| ~ member(ordered_pair(X0,sK7),X1)
| member(ordered_pair(X0,sK6),compose(X1,sK4))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl19_5 ),
inference(resolution,[],[f137,f192]) ).
fof(f749,plain,
( ! [X0,X1] :
( ~ ilf_type(sK7,set_type)
| ~ member(ordered_pair(X0,sK7),X1)
| member(ordered_pair(X0,sK6),compose(X1,sK4))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK6,set_type) )
| ~ spl19_5 ),
inference(forward_subsumption_resolution,[],[f742,f111]) ).
fof(f755,plain,
( ! [X0,X1] :
( ~ ilf_type(sK7,set_type)
| ~ member(ordered_pair(X0,sK7),X1)
| member(ordered_pair(X0,sK6),compose(X1,sK4))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) )
| ~ spl19_5 ),
inference(forward_subsumption_resolution,[],[f749,f111]) ).
fof(f761,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,sK7),X1)
| member(ordered_pair(X0,sK6),compose(X1,sK4))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) )
| ~ spl19_5 ),
inference(forward_subsumption_resolution,[],[f755,f111]) ).
fof(f766,definition,
( spl19_23
<=> ilf_type(sK4,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl19_23])],[avatar_definition]) ).
fof(f767,plain,
( ilf_type(sK4,binary_relation_type)
| ~ spl19_23 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f768,plain,
( ~ ilf_type(sK4,binary_relation_type)
| spl19_23 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f770,definition,
( spl19_24
<=> ! [X0,X1] :
( ~ member(ordered_pair(X0,sK7),X1)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(X0,sK6),compose(X1,sK4)) ) ),
introduced(definition,[new_symbols(definition,[spl19_24])],[avatar_definition]) ).
fof(f771,plain,
( ! [X0,X1] :
( member(ordered_pair(X0,sK6),compose(X1,sK4))
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(X0,sK7),X1) )
| ~ spl19_24 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f772,plain,
( ~ spl19_23
| spl19_24
| ~ spl19_5 ),
inference(avatar_split_clause,[],[f761,f190,f770,f766]) ).
fof(f774,definition,
( spl19_25
<=> ilf_type(sK3,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl19_25])],[avatar_definition]) ).
fof(f775,plain,
( ilf_type(sK3,binary_relation_type)
| ~ spl19_25 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f776,plain,
( ~ ilf_type(sK3,binary_relation_type)
| spl19_25 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f783,plain,
( ~ relation_like(sK4)
| spl19_23 ),
inference(resolution,[],[f768,f219]) ).
fof(f784,plain,
( ~ relation_like(sK3)
| spl19_25 ),
inference(resolution,[],[f776,f219]) ).
fof(f785,plain,
( ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| spl19_4 ),
inference(superposition,[],[f187,f732]) ).
fof(f800,plain,
relation_like(sK3),
inference(resolution,[],[f415,f103]) ).
fof(f801,plain,
relation_like(sK4),
inference(resolution,[],[f415,f104]) ).
fof(f804,plain,
( $false
| spl19_19 ),
inference(forward_subsumption_resolution,[],[f801,f502]) ).
fof(f805,plain,
spl19_19,
inference(avatar_contradiction_clause,[],[f804]) ).
fof(f806,plain,
( $false
| spl19_17 ),
inference(forward_subsumption_resolution,[],[f800,f493]) ).
fof(f807,plain,
spl19_17,
inference(avatar_contradiction_clause,[],[f806]) ).
fof(f812,plain,
( member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ spl19_4 ),
inference(forward_demodulation,[],[f188,f732]) ).
fof(f813,plain,
( $false
| ~ spl19_19
| spl19_23 ),
inference(forward_subsumption_resolution,[],[f783,f501]) ).
fof(f814,plain,
( ~ spl19_19
| spl19_23 ),
inference(avatar_contradiction_clause,[],[f813]) ).
fof(f815,plain,
( $false
| ~ spl19_17
| spl19_25 ),
inference(forward_subsumption_resolution,[],[f784,f492]) ).
fof(f816,plain,
( ~ spl19_17
| spl19_25 ),
inference(avatar_contradiction_clause,[],[f815]) ).
fof(f964,plain,
( ~ ilf_type(sK3,binary_relation_type)
| ~ member(ordered_pair(sK5,sK7),sK3)
| spl19_4
| ~ spl19_24 ),
inference(resolution,[],[f771,f785]) ).
fof(f978,plain,
( ~ member(ordered_pair(sK5,sK7),sK3)
| spl19_4
| ~ spl19_24
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f964,f775]) ).
fof(f984,plain,
( $false
| spl19_4
| ~ spl19_6
| ~ spl19_24
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f978,f197]) ).
fof(f985,plain,
( spl19_4
| ~ spl19_6
| ~ spl19_24
| ~ spl19_25 ),
inference(avatar_contradiction_clause,[],[f984]) ).
fof(f1016,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(sK14(sK5,X0,sK3,X1),sK6),sK4)
| ~ ilf_type(sK14(sK5,X0,sK3,X1),member_type(sK1))
| ~ member(ordered_pair(sK5,X0),compose(sK3,X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK5,set_type) )
| ~ spl19_8 ),
inference(resolution,[],[f206,f135]) ).
fof(f1017,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(sK14(sK5,X0,sK3,X1),sK6),sK4)
| ~ ilf_type(sK14(sK5,X0,sK3,X1),member_type(sK1))
| ~ member(ordered_pair(sK5,X0),compose(sK3,X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK5,set_type) )
| ~ spl19_8
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1016,f775]) ).
fof(f1018,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(sK14(sK5,X0,sK3,X1),sK6),sK4)
| ~ ilf_type(sK14(sK5,X0,sK3,X1),member_type(sK1))
| ~ member(ordered_pair(sK5,X0),compose(sK3,X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK5,set_type) )
| ~ spl19_8
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1017,f111]) ).
fof(f1019,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(sK14(sK5,X0,sK3,X1),sK6),sK4)
| ~ ilf_type(sK14(sK5,X0,sK3,X1),member_type(sK1))
| ~ member(ordered_pair(sK5,X0),compose(sK3,X1))
| ~ ilf_type(X1,binary_relation_type) )
| ~ spl19_8
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1018,f111]) ).
fof(f1106,plain,
( ~ ilf_type(sK14(sK5,sK6,sK3,sK4),member_type(sK1))
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ ilf_type(sK4,binary_relation_type)
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type)
| ~ spl19_8
| ~ spl19_25 ),
inference(resolution,[],[f1019,f134]) ).
fof(f1107,plain,
( ~ ilf_type(sK14(sK5,sK6,sK3,sK4),member_type(sK1))
| ~ member(ordered_pair(sK5,sK6),compose(sK3,sK4))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type)
| ~ spl19_8
| ~ spl19_25 ),
inference(duplicate_literal_removal,[],[f1106]) ).
fof(f1108,plain,
( ~ ilf_type(sK14(sK5,sK6,sK3,sK4),member_type(sK1))
| ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type)
| ~ spl19_4
| ~ spl19_8
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1107,f812]) ).
fof(f1109,plain,
( ~ ilf_type(sK14(sK5,sK6,sK3,sK4),member_type(sK1))
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type)
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1108,f767]) ).
fof(f1110,plain,
( ~ ilf_type(sK14(sK5,sK6,sK3,sK4),member_type(sK1))
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK5,set_type)
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1109,f775]) ).
fof(f1111,plain,
( ~ ilf_type(sK14(sK5,sK6,sK3,sK4),member_type(sK1))
| ~ ilf_type(sK6,set_type)
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1110,f111]) ).
fof(f1112,plain,
( ~ ilf_type(sK14(sK5,sK6,sK3,sK4),member_type(sK1))
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1111,f111]) ).
fof(f1113,plain,
( ~ member(sK14(sK5,sK6,sK3,sK4),sK1)
| empty(sK1)
| ~ ilf_type(sK1,set_type)
| ~ ilf_type(sK14(sK5,sK6,sK3,sK4),set_type)
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(resolution,[],[f1112,f131]) ).
fof(f1114,plain,
( ~ member(sK14(sK5,sK6,sK3,sK4),sK1)
| ~ ilf_type(sK1,set_type)
| ~ ilf_type(sK14(sK5,sK6,sK3,sK4),set_type)
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1113,f127]) ).
fof(f1115,plain,
( ~ member(sK14(sK5,sK6,sK3,sK4),sK1)
| ~ ilf_type(sK1,set_type)
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1114,f111]) ).
fof(f1116,plain,
( ~ member(sK14(sK5,sK6,sK3,sK4),sK1)
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1115,f111]) ).
fof(f1623,plain,
( ! [X0,X1] :
( ~ ilf_type(sK4,binary_relation_type)
| ~ ilf_type(sK3,binary_relation_type)
| member(sK14(sK5,sK6,sK3,sK4),X0)
| ~ ilf_type(sK4,relation_type(X0,X1)) )
| ~ spl19_4 ),
inference(resolution,[],[f671,f812]) ).
fof(f1640,plain,
( ! [X0,X1] :
( ~ ilf_type(sK3,binary_relation_type)
| member(sK14(sK5,sK6,sK3,sK4),X0)
| ~ ilf_type(sK4,relation_type(X0,X1)) )
| ~ spl19_4
| ~ spl19_23 ),
inference(forward_subsumption_resolution,[],[f1623,f767]) ).
fof(f1644,plain,
( ! [X0,X1] :
( ~ ilf_type(sK4,relation_type(X0,X1))
| member(sK14(sK5,sK6,sK3,sK4),X0) )
| ~ spl19_4
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1640,f775]) ).
fof(f1647,plain,
( member(sK14(sK5,sK6,sK3,sK4),sK1)
| ~ spl19_4
| ~ spl19_23
| ~ spl19_25 ),
inference(resolution,[],[f1644,f104]) ).
fof(f1648,plain,
( $false
| ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(forward_subsumption_resolution,[],[f1647,f1116]) ).
fof(f1649,plain,
( ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(avatar_contradiction_clause,[],[f1648]) ).
cnf(s5,plain,
( spl19_4
| spl19_5 ),
inference(sat_conversion,[],[f193]) ).
cnf(s6,plain,
( spl19_4
| spl19_6 ),
inference(sat_conversion,[],[f198]) ).
cnf(s8,plain,
( ~ spl19_4
| spl19_8 ),
inference(sat_conversion,[],[f207]) ).
cnf(s16,plain,
( ~ spl19_5
| ~ spl19_23
| spl19_24 ),
inference(sat_conversion,[],[f772]) ).
cnf(s18,plain,
spl19_19,
inference(sat_conversion,[],[f805]) ).
cnf(s19,plain,
spl19_17,
inference(sat_conversion,[],[f807]) ).
cnf(s20,plain,
( ~ spl19_19
| spl19_23 ),
inference(sat_conversion,[],[f814]) ).
cnf(s21,plain,
( ~ spl19_17
| spl19_25 ),
inference(sat_conversion,[],[f816]) ).
cnf(s28,plain,
( spl19_4
| ~ spl19_6
| ~ spl19_24
| ~ spl19_25 ),
inference(sat_conversion,[],[f985]) ).
cnf(s38,plain,
( ~ spl19_4
| ~ spl19_8
| ~ spl19_23
| ~ spl19_25 ),
inference(sat_conversion,[],[f1649]) ).
cnf(s39,plain,
spl19_25,
inference(rat,[],[s21,s19]) ).
cnf(s40,plain,
spl19_23,
inference(rat,[],[s20,s18]) ).
cnf(s44,plain,
( ~ spl19_5
| spl19_24 ),
inference(rat,[],[s16,s40]) ).
cnf(s47,plain,
spl19_4,
inference(rat,[],[s44,s28,s5,s6,s39]) ).
cnf(s48,plain,
~ spl19_8,
inference(rat,[],[s38,s39,s40,s47]) ).
cnf(s53,plain,
$false,
inference(rat,[],[s8,s48,s47]) ).
fof(f1650,plain,
$false,
inference(avatar_sat_refutation,[],[s53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET684+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 02:35:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.86/1.55 % (4099959)Detected formulas, will run a generic FOF schedule.
% 3.86/1.55 % (4099964)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=673716501:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.86/1.55 % (4099965)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1786996636:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.86/1.55 % (4099966)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1718932699:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.86/1.55 % (4099967)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2378731019:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.86/1.55 % (4099970)dis-21_1_sil=8000:lcm=predicate:random_seed=603601961:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.86/1.55 % (4099968)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3906463961:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.86/1.55 % (4099967)Refutation not found, incomplete strategy
% 3.86/1.55 % (4099967)------------------------------
% 3.86/1.55 % (4099967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (4099967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (4099967)CaDiCaL version: 2.1.3
% 3.86/1.55 % (4099967)Termination reason: Refutation not found, incomplete strategy
% 3.86/1.55 % (4099967)Time elapsed: 0.004 s
% 3.86/1.55 % (4099967)Peak memory usage: 88 MB
% 3.86/1.55 % (4099967)Instructions burned: 4 (million)
% 3.86/1.55 % (4099969)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2265994350:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.86/1.55 % (4099968)Instruction limit reached!
% 3.86/1.55 % (4099968)------------------------------
% 3.86/1.55 % (4099968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (4099968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (4099968)CaDiCaL version: 2.1.3
% 3.86/1.55 % (4099968)Termination reason: Instruction limit
% 3.86/1.55 % (4099968)Termination phase: Saturation
% 3.86/1.55 % (4099968)Time elapsed: 0.072 s
% 3.86/1.55 % (4099968)Peak memory usage: 88 MB
% 3.86/1.55 % (4099968)Instructions burned: 120 (million)
% 3.86/1.55 % (4099970)Instruction limit reached!
% 3.86/1.55 % (4099970)------------------------------
% 3.86/1.55 % (4099970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (4099970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (4099970)CaDiCaL version: 2.1.3
% 3.86/1.55 % (4099970)Termination reason: Instruction limit
% 3.86/1.55 % (4099970)Termination phase: Saturation
% 3.86/1.55 % (4099970)Time elapsed: 0.076 s
% 3.86/1.55 % (4099970)Peak memory usage: 90 MB
% 3.86/1.55 % (4099970)Instructions burned: 130 (million)
% 3.86/1.55 % (4099969)Instruction limit reached!
% 3.86/1.55 % (4099969)------------------------------
% 3.86/1.55 % (4099969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (4099969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (4099969)CaDiCaL version: 2.1.3
% 3.86/1.55 % (4099969)Termination reason: Instruction limit
% 3.86/1.55 % (4099969)Termination phase: Saturation
% 3.86/1.55 % (4099969)Time elapsed: 0.102 s
% 3.86/1.55 % (4099969)Peak memory usage: 90 MB
% 3.86/1.55 % (4099969)Instructions burned: 139 (million)
% 3.86/1.55 % (4099978)lrs+10_1_sil=8000:sp=occurrence:random_seed=1633062408:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.86/1.55 % (4099979)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2243858761:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.86/1.55 % (4099967)------------------------------
% 3.86/1.55 % (4099967)------------------------------
% 3.86/1.55 % (4099978)First to succeed.
% 3.86/1.55 % (4099978)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4099959"
% 3.86/1.55 % (4099980)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4273947667:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.86/1.55 % (4099979)Instruction limit reached!
% 3.86/1.55 % (4099979)------------------------------
% 3.86/1.55 % (4099979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (4099979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (4099979)CaDiCaL version: 2.1.3
% 3.86/1.55 % (4099979)Termination reason: Instruction limit
% 3.86/1.55 % (4099979)Termination phase: Saturation
% 3.86/1.55 % (4099979)Time elapsed: 0.083 s
% 3.86/1.55 % (4099979)Peak memory usage: 90 MB
% 3.86/1.55 % (4099979)Instructions burned: 157 (million)
% 3.86/1.55 % (4099983)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3615207727:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.86/1.55 % (4099985)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3386609759:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.86/1.55 % (4099985)Refutation not found, incomplete strategy
% 3.86/1.55 % (4099985)------------------------------
% 3.86/1.55 % (4099985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (4099985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (4099985)CaDiCaL version: 2.1.3
% 3.86/1.55 % (4099985)Termination reason: Refutation not found, incomplete strategy
% 3.86/1.55 % (4099985)Time elapsed: 0.005 s
% 3.86/1.55 % (4099985)Peak memory usage: 88 MB
% 3.86/1.55 % (4099985)Instructions burned: 5 (million)
% 3.86/1.55 % (4099980)Instruction limit reached!
% 3.86/1.55 % (4099980)------------------------------
% 3.86/1.55 % (4099980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.55 % (4099980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.55 % (4099980)CaDiCaL version: 2.1.3
% 3.86/1.55 % (4099980)Termination reason: Instruction limit
% 3.86/1.55 % (4099980)Termination phase: Saturation
% 3.86/1.55 % (4099980)Time elapsed: 0.205 s
% 3.86/1.55 % (4099980)Peak memory usage: 91 MB
% 3.86/1.55 % (4099980)Instructions burned: 326 (million)
% 3.86/1.55 % (4099978)Refutation found. Thanks to Tanya!
% 3.86/1.55 % SZS status Theorem for theBenchmark
% 3.86/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.47/1.74 % (4099978)------------------------------
% 5.47/1.74 % (4099978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.74 % (4099978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.74 % (4099978)CaDiCaL version: 2.1.3
% 5.47/1.74 % (4099978)Termination reason: Refutation
% 5.47/1.74 % (4099978)Time elapsed: 0.044 s
% 5.47/1.74 % (4099978)Peak memory usage: 90 MB
% 5.47/1.74 % (4099978)Instructions burned: 67 (million)
% 5.47/1.74 % (4099978)------------------------------
% 5.47/1.74 % (4099978)------------------------------
% 5.47/1.74 % (4099959)Success in time 0.693 s
% 5.47/1.74 % Vampire exiting
%------------------------------------------------------------------------------